You are 60 years old. Currently, you have $10,000 invested in an IRA and have ju

Question

You are 60 years old. Currently, you have $10,000 invested in an IRA and have just received a lum-sum distribution of $50,000 from a pension plan, which you roll over into an IRA. You continue to make $2,000 annual payments to the regular IRA and expect to earn 9% on those funds until you start withdrawing the money at age 70 (ie after 10 years). The IRA rollover will earn 9% for the same duration.
a) How much will you have when you start to make withdrawls at age 70?
b) If your funds continue to earn 9% annually and you withdraw $17,000 annually, how long will it take to exhaust your funds?
c) If your funds continue to earn 9% annually and your life expectancy is 18 years, what is the maximum you may withdraw each year?

Please show all your work.

Thank you.

Explanation / Answer

(a) Future value (at age 70) = (50000+10000)1.0910+(2000/0.09)(1.0910-1)

Future value (at age 70) = 172427.68

(b) Total PV of money withdrawn in the future = Present value at age 70 (answer in (a) )

172427.68 = (17000/0.09)(1-1/1.09n)

Solve for n = 28.3 years ---> (28 years)

(c) Let A = money withdrawn each year

172427.68 =  (A/0.09)(1-1/1.0918)

Solve for A =19693.36

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